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CHAPTER - 2

REVIEW OF LITERATURE

2.1 INTRODUCTION

Recently, there is a great interest in active vibration control of

beam, plate and shell structures. Vibration is an undesirable

phenomenon in aerospace, mechanical and civil systems. In particular

aerospace structures (curved/ flat/ thin walled) may experience

adverse aerodynamic environments, which induce random vibrations.

The concept of active vibration control is very much useful to enhance

the performance in such structures. Electro-mechanically coupled PZT

materials are now considered as actuators and sensors in many active

vibration control applications.

A number of studies are reported on the modeling of electro-

mechanical coupling with different structural applications in active

vibration control. A few experimental studies are also available on the

active vibration control of composite beams and plates. A thorough

understanding of electro mechanical coupling, control concepts is

prerequisites for present research. For critically assessing the

available literature relevant to the present research problem, the

complete literature review process is carried out.

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2.2 SOME STUDIES ON PIEZOELECTRICITY AND PIEZOCERAMICACTUATORS

Pierre and Jacques Curie brothers (1880), examined the

piezoelectric effect on crystal materials, (quartz, Rochelle salt) which

have the ability to produce electrical charges in response to externally

applied forces. This effect they named as "Piezoelectricity", after the

Greek word “piezein”, which means to squeeze or press.

Lippmann (1881), deduced mathematically the converse

piezoelectric effect from the fundamental thermodynamic principles.

This phenomenon illustrates that the application of an electrical field

creates a mechanical stress.

Cady’s (1946), worked on development of piezoelectric devices.

These developments led to numerous ceramic materials with better

piezoelectric properties. The discovery of piezoelectricity in PZT in the

late 1960’s increased the number of applications for industrial use.

Hagood and Bent (1993), developed an alternative actuators to

existing commercial actuator by combining the interdigitated

electrodes (IDEs) with piezoceramics. The circular cross-section PZT

fibers of the Active Fiber Composite (AFC) had very little contact area

between the interdigitated electrodes and the fibers. Due to this the

transfer of the electric field into the PZT fibers is inefficient and also

the AFC operates at very high voltage.

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Bent et al. (1994), developed the first generation of

piezocomposite actuators. They are the remedy for the significant

drawbacks of monolithic piezoceramics. Piezo Fiber Composite (PFC)

combines piezoceramic materials and additional inactive components

in a specific structure to form an overall actuator/sensor package.

Adriaens et al. (2000), presented An electromechanical piezo

model, based on physical principles. In this model, a first-order

differential equation is adopted to describe the hysteresis effect, and a

partial differential equation is used to describe the mechanical

behavior.

Wilkie et al. (2000), developed the Macro Fiber Composite (MFC)

at NASA Langley Research Center. The MFC is a piezoelectric fiber

composite which has the rectangular cross-section and unidirectional

piezoceramic fibers embedded in the polymer matrix and uses the

interdigitated electrode. Unlike the AFC, the rectangular PZT fiber of

the MFC ensured the maximum contact area between the PZT fibers

and the interdigitated electrodes.

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2.3 FE FORMULATION WITH PIEZOELECTRIC COUPLING- AREVIEW

Allik and Hughes (1970), presented a finite element formulation

which includes the piezoelectric and electroelastic effect. The

dynamical matrix equation of electroelasticity was formulated by them

to develop tetrahedral finite element.

Macneal (1978), formulated a four-noded quadrilateral shell

element, called QUAD4, which was based on isoparametric principles

with modifications which relax excessive constraints.

Naganarayana and Prathap (1989) reported on force and

moment corrections for the warped four-node quadrilateral plane shell

element. The element stiffnesses were generated for a ‘mean plane’

equidistant from the four nodes, and are corrected by introducing

equilibrated forces and moments.

Chandrashekhara and Agarwal (1993), presented a finite

element formulation for modeling the behavior of laminated

composites with integrated piezoelectric sensors and actuators. This

model they validated for both continuous and segmented piezoelectric

elements that can be either surface bonded or embedded in the

laminated plate.

Samanta et al. (1996), formulated a generalized finite element

procedure for active vibration control of a laminated plate with

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piezoelectric laminas. They derived an eight-noded shear deformable

plate element. Also the vibration control was studied by them with a

simple feedback control strategy.

Varadan et al. (1996), Discussed the three dimensional finite

element model to predict the effects of both active and passive

damping of a vibrating structure. A cantilever structure made of

viscoelastic core sandwiched between piezoelectric actuator and

sensor was considered by them for the closed loop control analysis.

They have showed that the hybrid concept introduces better damping

than purely passive or active system.

Chang et al.(1996), derived general finite element formulations for

piezoelectric sensors and actuators by using the virtual work

principle. The amplitude-frequency and the phase-frequency

characteristics of the closed-loop system were studied by them.

Chen et al. (1997), employed a plate finite element to model the

structural system parameters and used a negative velocity feedback

control law to demonstrate the active vibration control by piezoelectric

actuators. Using state-space equations, damped frequencies and

damping ratio were derived by them numerically.

Han et al (1997) experimentally studied active vibration control of

composite structures with a piezo-ceramic actuator and a piezo-film

sensor using the classical laminated beam theory and Ritz method, an

analytical model of the laminated composite beam with piezoelectric

sensors and actuators.

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Benjeddou et al. (1997), presented a finite element model for

adaptive sandwich beams to deal with either extension or shear

actuation mechanism. For both configurations, an electric field is

applied through thickness of the piezoelectric layers.

Saravanos (1997), developed mixed laminate theory for

piezoelectric shells in curvilinear coordinates that combines single-

layer assumptions for the displacements. Mechanics for the analysis

of laminated composite shells with piezoelectric actuators and sensors

were presented.

Baruch and Abramovich (1997), extended the formulation of

Miller et al. (1995) to include the material and geometric variation. The

piezoelectric actuator forces were represented as equivalent

mechanical loads in the equations of motion in a generalised form so

that the solution could be found using well-established approximate

methods.

Batra and Liang (1997) presented an analytical solution for the

vibration control of a simply supported rectangular plate expanding

displacement functions as Fourier series.

Clinton et al. (1998), studied coupled structure-actuator-sensor

interactions and developed both analytical and numerical models to

realize the so called smart or adaptive structures.

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Liu et al.(1999), presented a finite element formulation to model the

dynamic as well as static response of laminated composite plates

containing integrated piezoelectric sensors and actuators subjected to

both mechanical and electrical loadings. The formulation was based

on the classical laminated plate theory and Hamilton’s principle. A

four node non-conforming rectangular plate bending element was

implemented by them for the analysis. The influence of stacking

sequence and position of sensors/actuators on the response of the

plate was evaluated.

Dogan and Vaicaitis (1999) developed analytical model for active

control of nonlinear flexural vibrations of cylindrical shells under

random excitation. A velocity feedback control scheme was integrated

into the governing equations of motion using discrete surface-bonded

piezoelectric materials as collocated sensors/actuators.

Benjeddou (2000), has conducted survey on the advances and

trends in the formulations and applications of the finite element

modeling of adaptive structural elements focusing on the development

of adaptive piezoelectric finite elements.

Azzouz et al. (2001), have developed a triangular piezoelectric

shallow shell element for analyzing structures with MFC/AFC

actuators and compared the performance of the MFC actuator with

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that of the traditional PZT actuator. Developed element was used to

investigate the effect of PZT fiber orientation on acoustic and

structural vibration control of plate and shells.

Wang et al.(2001), investigated the vibration control of smart

piezoelectric composite plates and the effect of the stretching-bending

coupling of the piezoelectric sensor/actuator pairs on the system

stability of smart composite plates. Based on first-order shear theory

and consistent methodology, a smart isoparametric finite element was

formulated and the classical negative velocity feedback control method

is adopted for the active vibration control analysis of smart composite

plates with bonded or embedded distributed piezoelectric sensors and

actuators.

Balamurugan and Narayanan (2001), proposed the mechanics

for the coupled analysis of piezolaminated plate and piezolaminated

curvilinear shell structures and their vibration control performance. A

plate/shell structure with thin PZT piezoceramic layers embedded on

top and bottom surfaces to act as distributed sensor and actuator was

considered.

Chad Landis (2001), presented a new finite-element formulation

for the solution of electromechanical boundary value problems. As

opposed to the standard formulation that uses scalar electric potential

as nodal variables, this new formulation implements a vector potential

from which components of electric displacement are derived.

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Bernadou and Christophe (2003), developed a two-dimensional

modelization of piezoelectric thin shells the approximation of the

second formulation by a conforming finite element method was

analyzed.

Singh et al. (2003), described Some efficient strategies for the

active control of vibrations of a beam structure using piezoelectric

materials. The control algorithms have been implemented for a

cantilever beam model developed using finite element formulation.

Lee and Yao (2003), experimentally studied the active vibration

control of structures subject to external excitations using piezoelectric

sensors and actuators. A simply supported plate and a curved panel

were used as the structures in experiments. The Independent Modal

Space Control (IMSC) approach was employed for the

controller design.

Raja et al. (2004), modeled a coupled piezoelectric field with an

expansion strain in the numerical formulation to analyze

piezohygrothermoelastic laminated plates and shells. Finite element

actuator and sensor equations are derived using a nine-noded field

consistent shallow shell element.

Robaldo et al. (2006), presented finite element for the dynamic

analysis of laminated plates embedding piezoelectric layers based on

the principle of virtual displacements (PVD) and a unified formulation.

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The full coupling between the electric and mechanical fields was

considered. Numerical results have been given by them for the free-

vibrations frequencies of simply supported plates embedding

piezoelectric layers.

Balamurugan and Narayanan (2008), presented formulation of

a nine-noded piezolaminated degenerated shell finite element for

modeling and analysis of multilayer composite general shell structures

with bonded/embedded distributed piezoelectric sensors and

actuators.

Guennam and Luccioni (2009), developed a piezoelectric multi-

lamina shell FE to model for thin walled structures with piezoelectric

fiber composites polarized with interdigitated electrodes (PFCPIE). A

new scheme for the interpolation of the electric field was presented.

Ivelin V. Ivanov (2011), modelled Active Fibre Composites (AFC)

by piezo-electric Finite Elements (FEs) and their effective properties

are determined by FE analysis. Dynamic behaviour of a smart

composite structure was simulated by them in Finite Element.

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2.4 VIBRATION CONTROL USING MFC ACTUATORS

Balas (1978) and Meirovitch et al. (1983), were among the first

to present the vibration control procedures for the large flexible

structural systems.

Aubrun (1980), presented the collocated or localized

interconnection concept for structural vibration control with

distributed actuators and sensors.

Meirovitch (1983) proposed coupled control. A unique and

globally optimal closed-form solution to the linear optimal control

problem of the distributed structure was presented.

Crawley & Luis (1987), presented the analytical and

experimental development of piezoelectric actuators as an element of

intelligent structure.

Tzou (1987) proposed a distributed active piezoelectric damper

and evaluated using analytical, experimental, and finite element

techniques for active vibration control of flexible structures via

converse piezoelectricity.

Baz and Poh (1988), presented the utilization of piezoelectric

actuators in controlling the structural vibrations of flexible beams. A

Modified Independent Modal Space Control (MIMSC) method was

presented for selecting the optimal location, control gains and

excitation voltage of the piezoelectric actuators.

Lammering (1991), focused on the finite element analysis of

shell structures with piezoelectric layers bonded on the surface. A

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finite element formulation taking the piezo-electric effect into account

was given and a finite shell element was presented.

Clark & Fuller (1991), have studied on panels, the vibration

control and its effect on the reduction of sound radiation. Active

structural acoustic control (ASAC) using conventional fine mass

dampers and PZT activators are currently emerging as a popular

solution for vibration induced noise control problems.

Hwang & chul park (1993), presented FE formulation for

vibration control of a laminated plate with piezoelectric

sensors/actuators. Classical laminate theory with the induced strain

actuation and Hamilton's principle are used to formulate the

equations of motion.

Tzou and Hollkamp (1994), proposed a scheme based on

collocated spatially distributed actuators/sensors assembly to achieve

independent control of natural modes of a structural system. The

actuators/sensors were spatially shaped to capture the response and

control of a particular mode of a laminated cantilever beam.

Miller et al. (1995), developed a selective modal control strategy

based on Lyapunov’s second method for piezolaminated anisotropic

thin shells. The proposed scheme was used to demonstrate

simultaneous sensing and actuation of a particular mode with

arbitrarily chosen modal participation factors.

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Baz and Poh (1996), proposed an active control scheme based

on Independent Modal Space Control (IMSC) for a flexible beam with

optimally placed piezoelectric actuators.

Yang and bian (1996), experimentally demonstrated that,

without sacrificing the structural advantages, the piezoelectric

element embedded in composite laminated structures can be applied

both as the in situ vibration sensor and as the vibration suppression

actuator.

Del Rosario et al. (1998), reported a study on vibration control of

thin shells with piezoelectric layers. The shell governing equations

were derived based on Donnell-Mushtari theory. Closed form solutions

of the shell dynamics and controls were presented using Galerkin

expansion and LQR based control strategy. Jung Woo Sohn et al.

studied active vibration control of smart hull structure using

piezoelectric composite actuators.

Kim et al. (2000), designed distributed sensor and actuator for

the active vibration control of shell structure. To prevent the adverse

effect of spillover, distributed modal sensor/actuator system was

established by optimizing the electrode pattern and the lamination

angle of polyvinylidene fluoride (PVDF).

Bevan (2001), has proposed a modified GA based optimal

placement scheme for MFC actuator using LQR control strategy.

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Further he has examined the performance of the MFC actuator in

vibration and acoustic control of carved and flat panels.

Jha and Inman (2003), modeled the dynamics of a lightweight,

inflatable shell structure commonly used in telecommunications

satellites and other space-based structures and also experimentally

investigated the suitability of using the MFC for structural vibration

applications.

Williams et al. (2004), investigated the mechanical properties of

the MFC using the classical lamination theory. Nonlinear mechanical

behaviors of the MFC were studied by the experiment, and the linear

mechanical properties of the MFC were compared with the result of

the analytical method. In addition, Williams measured the nonlinear

actuation properties of the MFC under various loads. There are also

some researches for the application of the MFC to the structure.

Ruggerio et al. (2004), used several MFCs as both actuators

and sensors to measure the dynamic behavior of the inflatable

satellite structure and to control its vibration. The flexibility of the

MFC made for convenient attachment to the doubly-curved surface,

and it was found that MFC outperformed the other actuators.

Schultz and Hyer (2006), used the flexibility and high force

output of the MFC to snap-through an unsymmetric composite

laminate from one stable configuration to the other.

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Kovalovs et al. (2007), demonstrated experimentally the

application of MFC actuators in vibration control of aluminum beam

and metal music plate. The MFC’S are used, one as an exciter and

other as an actuator. ANSYS was used to model the structures with

thermal analogy for including the piezoelectric actuation.

Ro et al. (2007), adopted a LQR based feedback control strategy

using MFC actuators to suppress the flexural vibration of cycle handle

bar to establish the natural frequencies and mode shapes.

Shon and Choi (2008), used GA to optimally place MFC

actuators on cylindrical aluminum shell and conducted active

vibration control experiments. A Lagrangion based theoretical

formulation was made by them to capture the dynamics of the shell

including the electro-mechanical couplings of MFC actuators.

Kwak et al. (2009), performed theoretical and experimental

investigations on aluminum cylindrical shell vibration control using

the MFC actuators. The theoretical model was developed by them

using Rayleigh Ritz approximation and the strain displace relations

are established based on Donnel-Mushtari theory. First three modes

of the cylinder are successfully controlled by a positive position

feedback, implemented in DS1104.

Rolf Paradies and Paolo Ciresa (2009), implemented Piezoelectric

macro fiber composites (MFCs) actuators into an active composite

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wing. Dynamic tests were also performed by them on a sandwich wing

of the same size with conventional aileron control for comparison.

Eliza Munteanu and Ioan Ursu (2010), obtained control law

LQG/LTR (Linear Quadratic Gaussian/ Loop Transfer Recovery).The

robustness characteristics of the optimal control LQR (Linear

Quadratic Regulator) are recovered by the Kalman filter applying a

special construction for the estimator.

Alibeigloo and Kani (2010), studied vibration problem of

multilayered shells with embedded piezoelectric layers. An approach

combining the state space method and the differential quadrature

method (DQM) was used for shell vibration control

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2.5 BUCKLING AND SHAPE CONTROL OF COMPOSITE

CYLINDRICAL SHELL PANELS

Sobels et al. (1976), studied buckling of cylindrical panels under

axial compression. The effect of boundary conditions and panel width

on the axially compressive buckling behavior of un-stiffened, isotropic,

circular cylindrical panels was investigated.

Becker et al. (1982), conducted experimental investigation on the

instability of composite cylindrical panels. A detailed description of

test methods and analytical procedures used to evaluate the buckling

of composite curved panels are presented.

Zhang and Matthews (1983), studied Initial buckling of curved

panels of generally layered composite materials. An initial buckling

analysis for cylindrically curved panels made of generally layered

composite materials was presented. The influence of curvature, fibre

angles, stacking sequence and panel aspect ratios on buckling was

investigated.

Reddy (1984), reported on exact solutions of moderately thick

laminated shells. Static and dynamic behavior of shell was captured.

An extension of the Sanders shell theory for doubly curved shells to a

shear deformation theory of laminated shells was presented.

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Jun and Hong (1988), presented formulation of the geometrically

nonlinear finite element procedure based on an updated Lagrangian

on the buckling behavior of laminated composite cylindrical panels

under axial compression.

Sheinmany et al. (1992), developed PBCOMP program for buckling

and post buckling of stiffened laminated curved panels. The program

was based on the von Karman kinematic approach and uses the eigen

functions of an isotropic beam in the longitudinal direction and finite

differences in the lateral direction.

Sai Ram et al. (1992), studied hygrothermal effects on the buckling

of laminated composite Plates. The effects of moisture and

temperature on the static instability of laminated composite plates are

investigated.

Geie and Singh (1997), studied some simple solutions for buckling

loads of thin and moderately thick cylindrical shells and panels of

laminated composite material.

Mandal et.al. (2000), conducted experiments on the buckling of

thin cylindrical shells under axial compression. Simple experiments

such as self-weight buckling of thin, open-top, fixed-base, small-scale

silicone rubber cylindrical shells are presented.

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Girsh, and Ramachandra (2008), studied the stability and

vibration behavior of composite cylindrical shell panels under axial

compression and secondary loads. The influence of initial geometric

imperfection, temperature field, and lateral pressure loads, and

mechanical edge loads on the static response and vibration behavior of

the shell panel.

Himayat Ullah (2009), reported on buckling of thin-walled

cylindrical shells under axial compression. He concluded that the

effects of non-Linearity and geometric imperfections are responsible

for the mismatch between theoretical and experimental results.

Raja et al.(2011) studied the use of surface bonded and embedded

piezoelectric composite actuators through a numerical study by

applying the isoparametric finite element approach to idealize

extension-bending and shear-bending couplings due to piezoelectric

actuations for deflection and vibration control of laminated plates.

2.6 SCOPE OF THE PRESENT WORK

Finite element and many theoretical analysis employed in active

vibration control analysis have been reported on amplitude and shape

control for beams and plates. The active vibration control of shell

structures is still very much limited. There is further scope for

research on developing either analytical or numerical models on

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composite cylindrical and spherical shells. Macro Fiber Composite

(MFC) produces more induced actuation strain than transerversely

polarized monolithic piezoelectric ceramic patch because of In-plane

poling property of MFC with interdigitated electrodes. Further MFC is

flexible and therefore more suitable to the curved structures.

The review of literature shows that not much attention has been

given to this promising area where MFC actuator was employed for

vibration control of panels and shells. As smart structure concepts are

increasingly exploited in aerospace composite structural systems,

active vibration control is a more promising technology today and with

active materials having distributed actuation and sensing capabilities.

However, all the developed and developing concepts using the new or

existing analytical and numerical models must be experimented to

convert the theoretical concept into a promising technology.

Some experiments were earlier reported on the active vibration

control in the literature using feedback, feed forward and neural

network based controllers. However, there is a need to develop smart

structure concepts to use the piezoelectric actuation effectively to

control different elastic modes (bending or torsion) by properly

selecting the type of control i.e., displacement or velocity.

Displacement control with piezoelectric actuation will stiffen the

structure and bring down the amplitude by shifting the closed loop

system frequency. On the other hand, velocity control develops a

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resistive force that will help to improve the system damping. Thus by

properly controlling a state (displacement or velocity), a desired

structural response can be enforced on the structural system.

The review of relevant literature has brought the following

observations.

Use of the MFC actuators for directional actuation is efficient

Studies on isotropic beams, plates are successfully

conducted

Beam, plate, triangular shell finite elements are proposed

with MFC actuators

However,

The study on composite shell with piezoelectric composites

(MFC) is very much limited

An efficient electromechanically coupled shell element

validated with experiment may be required

Evaluation of in plane actuation on the vibration of coupled

elastic membrane – bending modes needs further attention

Control of in-plane disturbances (buckled shell shape

control) by piezoelectric actuation needs to be evaluated; so

that the design of wing panels, panel flutter, dynamic

buckling kinds of problems must be addressed

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Keeping these objectives, a shear flexible field consistent four

noded facet shell element is proposed in the present work. Further a

deep cylindrical shell made of CFRP has been fabricated and

instrumented with three MFC actuators and three PZT patch sensors.

A state feedback LQG controller is implemented in DS1104 DSP board

and both modal and selective control feedback strategies are

demonstrated.